scholarly journals Deformed Kac–Moody algebra and noncommutative Fermi theory in two dimensions

2021 ◽  
pp. 2150189
Author(s):  
M. W. AlMasri ◽  
M. R. B. Wahiddin
Keyword(s):  
Higher Order ◽  
Two Dimensions ◽  
Algebraic Structures ◽  
Fermi Theory ◽  
Moody Algebra ◽  
Higher Order Corrections

Starting from noncommutative Fermi theory in two dimensions, we construct a deformed Kac–Moody algebra between its vector and chiral currents. The higher-order corrections to the deformed Kac–Moody algebra are explicitly calculated. We observe that the ordinary Schwinger terms are not affected by noncommutativity. Finally we conclude that the deformed Kac–Moody algebra can be given in term of ordinary Kac–Moody algebra plus infinitely many Lie algebraic structures at each nonzero power of the antisymmetric coefficient [Formula: see text].

Some applications of the revisited approximate next-to-leading higher order corrections in QCD

2015 ◽  
Vol 30 (11) ◽  
pp. 1550047
Author(s):  
N. Mebarki ◽  
M. R. Bekli ◽  
H. Aissaoui
Keyword(s):  
Higher Order ◽  
Higher Order Corrections

Using the prescription and techniques of the soft and/or collinear gluon approach developed in Refs. 1–5 and revisited in Ref. 6, applications to some hadronic subprocesses are considered and approximate QCD higher order contributions are determined.

scholarly journals Nonlinear higher-order spectral solution for a two-dimensional moving load on ice

2009 ◽  
Vol 621 ◽  
pp. 215-242 ◽  
Author(s):  
FÉLICIEN BONNEFOY ◽  
MICHAEL H. MEYLAN ◽  
PIERRE FERRANT
Keyword(s):  
Critical Speed ◽  
Moving Boundary ◽  
Moving Load ◽  
Phase Speed ◽  
Nonlinear Effects ◽  
Higher Order ◽  
Two Dimensions ◽  
Linear Solution ◽  
Nonlinear Solution ◽  
Bernoulli’S Equation

We calculate the nonlinear response of an infinite ice sheet to a moving load in the time domain in two dimensions, using a higher-order spectral method. The nonlinearity is due to the moving boundary, as well as the nonlinear term in Bernoulli's equation and the elastic plate equation. We compare the nonlinear solution with the linear solution and with the nonlinear solution found by Parau & Dias (J. Fluid Mech., vol. 460, 2002, pp. 281–305). We find good agreement with both solutions (with the correction of an error in the Parau & Dias 2002 results) in the appropriate regimes. We also derive a solitary wavelike expression for the linear solution – close to but below the critical speed at which the phase speed has a minimum. Our model is carefully validated and used to investigate nonlinear effects. We focus in detail on the solution at a critical speed at which the linear response is infinite, and we show that the nonlinear solution remains bounded. We also establish that the inclusion of nonlinearities leads to significant new behaviour, which is not observed in the linear solution.

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